<h2>Problem 208</h2>
<div style="color:#666;font-size:80%;">12 September 2008</div><br />
<div class="problem_content">
<p>A robot moves in a series of one-fifth circular arcs (72&deg;), with a free choice of a clockwise or an anticlockwise arc for each step, but no turning on the spot.</p>

<p>One of 70932 possible closed paths of 25 arcs starting northward is</p>
<div style="text-align:center;">
<img src="http://projecteuler.net/project/images/p_208_robotwalk.gif" alt="" />
</div>

<p>Given that the robot starts facing North, how many journeys of 70 arcs in length can it take that return it, after the final arc, to its starting position?<br />
<!--(Journeys are allowed to return multiple times to the start.)-->
(Any arc may be traversed multiple times.) 
</p>

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